Question

What is the correct classification of the system of equations below? 5x + 6y = 1 y = -5x + 6 A. parallel B. coincident C. intersecting

Answer 1

Answer: OPTION C.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the system  of equations:

$\left \{ {{5x + 6y = 1} \atop {y = -5x + 6}} \right.$

Solve for "y" from the first equation in order to write it in Slope-Intercept form:

$5x + 6y = 1\\\\6y=-5x+1\\\\y=-\frac{5}{6}x+\frac{1}{6}$

Since the lines have different slopes, they cannot be parallel or coincident. Therefore, they are Intersecting.